Anomalous Roughening in Experiments of Interfaces in Hele-Shaw Flows with Strong Quenched Disorder

TL;DR

This study experimentally investigates anomalous kinetic roughening in oil-air interfaces within a Hele-Shaw cell with strong quenched disorder, revealing how local velocities and coupling lead to anomalous scaling behaviors.

Contribution

It provides the first detailed experimental evidence of anomalous roughening in Hele-Shaw flows with strong quenched disorder, analyzing the effects of velocity, capillarity, and disorder persistence.

Findings

Measured specific scaling exponents for roughening.

Identified conditions where anomalous scaling appears or disappears.

Linked interface morphology and multiscaling to local velocity variations.

Abstract

We report experimental evidences of anomalous kinetic roughening in the stable displacement of an oil-air interface in a Hele-Shaw cell with strong quenched disorder. The disorder consists on a random modulation of the gap spacing transverse to the growth direction (tracks). We have performed experiments varying average interface velocity and gap spacing, and measured the scaling exponents. We have obtained beta=0.50, beta*=0.25, alpha=1.0, alpha_l=0.5, and z=2. When there is no fluid injection, the interface is driven solely by capillary forces, and a higher value of beta around beta=0.65 is measured. The presence of multiscaling and the particular morphology of the interfaces, characterized by high slopes that follow a L\'evy distribution, confirms the existence of anomalous scaling. From a detailed study of the motion of the oil--air interface we show that the anomaly is a consequence of different local velocities over tracks plus the coupling in the motion between neighboring tracks. The anomaly disappears at high interface velocities, weak capillary forces, or when the disorder is not sufficiently persistent in the growth direction. We have also observed the absence of scaling when the disorder is very strong or when a regular modulation of the gap spacing is introduced.